Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels
This work addresses the theoretical understanding of learning algorithms for researchers in machine learning, providing insights into when gradient descent offers benefits over kernel methods, though it is incremental in nature.
The paper investigates the comparative effectiveness of gradient descent on differentiable models versus tangent kernel methods, showing that under specific conditions gradient descent's success implies a weak learning advantage for tangent kernels, but can also succeed where tangent kernels fail to outperform random guessing.
We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial advantage over random guessing (a.k.a. weak learning), though this advantage might be very small even when gradient descent can achieve arbitrarily high accuracy. Complementing this, we show that without these conditions, gradient descent can in fact learn with small error even when no kernel method, in particular using the tangent kernel, can achieve a non-trivial advantage over random guessing.